# square wave frequency representation

New to this signals stuff and i'm confused about the frequency representation of the square wave. Correct me if i'm wrong, a periodic square wave is composed of odd harmonics sine waves which are multiples of the fundamental frequency, In the frequency domain this just represents decreasing impulses at every odd multiple of the fundamental frequency . What relation does the sinc function have with the square wave? and which is the correct spectral representation of the square wave? Thanks!

## 1 Answer

The transform of a single rectangular pulse is a Sinc function. Each added translation of that pulse adds a twisted repitition of that Sinc. The twist will equal 2 pi at all spectral distances that are odd integer multiples of the reciprocal of the repeat period. Repeat, and eventually all the twisted portions will all cancel out (form circles in the complex plane around zero) except at those points representing the odd harmonics. Thus an infinite repeating square wave will be left with only non-zero spectrum at odd harmonics in its transform.